Cohomogeneity one Kahler and Kahler-Einstein manifolds with one singular orbit II

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F20%3A50017267" target="_blank" >RIV/62690094:18470/20:50017267 - isvavai.cz</a>
Result on the web
<a href="https://link.springer.com/article/10.1007/s10455-019-09693-6" target="_blank" >https://link.springer.com/article/10.1007/s10455-019-09693-6</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10455-019-09693-6" target="_blank" >10.1007/s10455-019-09693-6</a>

Result language
angličtina
Original language name
Cohomogeneity one Kahler and Kahler-Einstein manifolds with one singular orbit II
Original language description
Podesta and Spiro (Osaka J Math 36(4):805-833, 1999) introduced a class of G-manifolds M with a cohomogeneity one action of a compact semisimple Lie group G which admit an invariant Kahler structure (g, J) ("standard G-manifolds") and studied invariant Kahler and Kahler-Einstein metrics on M. In the first part of this paper, we gave a combinatoric description of the standard non-compact G-manifolds as the total space M-phi of the homogeneous vector bundle M = G x (H) V -> S-0 = G/ H over a flag manifold S-0 and we gave necessary and sufficient conditions for the existence of an invariant Kahler-Einstein metric g on such manifolds M in terms of the existence of an interval in the T-Weyl chamber of the flag manifold F = G x (H) PV which satisfies some linear condition. In this paper, we consider standard cohomogeneity one manifolds of a classical simply connected Lie group G = SUn, Sp(n).Spin(n) and reformulate these necessary and sufficient conditions in terms of easily checked arithmetic properties of the Koszul numbers associated with the flag manifold S-0 = G/H. If this condition is fulfilled, the explicit construction of the Kahler-Einstein metric reduces to the calculation of the inverse function to a given function of one variable.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA18-00496S" target="_blank" >GA18-00496S: Singular spaces from special holonomy and foliations</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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